The subgroup fixing one of the 759 (= 3·11·23) octads of the Golay code or Steiner system is the octad group 24:A8, order 322560, with orbits of size 8 and 16. The linear group GL(4,2) has an exceptional isomorphism to the alternating group A8. The pointwise stabilizer O of an octad is an abelian group of order 16, exponent 2, each of whose involutions moves all 16 points outside the octad. The stabilizer of the octad is a split extension of O by A8.
|
|
The hexacode can be used to describe the Miracle Octad Generator of R. T. Curtis.
|
|
The Miracle Octad Generator is a 4x6 array of combinations describing any point in 24-dimensional space. It preserves all of the symmetries and maximal subgroups of the Mathieu group M24, namely the monad group, duad group, triad group, octad group, octern group, sextet group, trio group and duum group. It can therefore be used to study all of these symmetries.
|
|
In mathematics, the Miracle Octad Generator, or MOG, is a mathematical tool introduced by Rob T. Curtis for manipulating the Mathieu groups, binary Golay code and Leech lattice.
|
|
Any matrix in this conjugacy class has trace 0. A permutation matrix of shape 2818 can be shown to be conjugate to an octad; it has trace 8. This and its negative (trace −8) have a common centralizer of the form , a subgroup maximal in Co0.
|
|
John Horton Conway developed a 4 × 3 array known as the MiniMOG. The MiniMOG provides the same function for the Mathieu group M12 and ternary Golay code as the Miracle Octad Generator does for M24 and binary Golay code, respectively. Instead of using a quaternary hexacode, the MiniMOG uses a ternary tetracode.
|
|
The octet is a unit of digital information in computing and telecommunications that consists of eight bits. The term is often used when the term byte might be ambiguous, as the byte has historically been used for storage units of a variety of sizes. The term octad(e) for eight bits is no longer common.
|
|
Asci of Morchella elata, containing ascospores Sordaria fimicola ascus plus ascospore An ascospore is a spore contained in an ascus or that was produced inside an ascus. This kind of spore is specific to fungi classified as ascomycetes (Ascomycota). Ascospores are formed in ascus under optimal conditions. Typically, a single ascus will contain eight ascospores (or octad).
|
|
The lowercase letter o for octet is defined as the symbol for octet in IEC 80000-13 and is commonly used in languages such as French and Romanian, and is also combined with metric prefixes for multiples, for example ko and Mo. The usage of the term octad(e) for eight bits is no longer common.
|
|
Historically, in Western Europe, the term octad (or octade) was used to specifically denote 8 bits; however, this usage is no longer common. Early examples of usage exist in British, Dutch and German sources of the 1960s and 1970s, and throughout the documentation of Philips mainframe computers. Similar terms are triad for a grouping of three and decade for ten.
|
|
The subgroup M11 is the stabilizer of a point. W12 can be constructed from the affine geometry on the vector space F3×F3, an S(2,3,9) system. An alternative construction of W12 is the 'Kitten' of . An introduction to a construction of W24 via the Miracle Octad Generator of R. T. Curtis and Conway's analog for W12, the miniMOG, can be found in the book by Conway and Sloane.
|
|
Asci of Morchella elata, Phase contrast image There are 8 ascospores in each ascus of Sordaria fimicola. An ascus (plural asci; from Greek ' 'skin bag') is the sexual spore-bearing cell produced in ascomycete fungi. Each ascus usually contains eight ascospores (or octad), produced by meiosis followed, in most species, by a mitotic cell division. However, asci in some genera or species can occur in numbers of one (e.g.
|
|
Co0 has 4 conjugacy classes of involutions; these collapse to 2 in Co1, but there are 4-elements in Co0 that correspond to a third class of involutions in Co1. An image of a dodecad has a centralizer of type 211:M12:2, which is contained in a maximal subgroup of type 211:M24. An image of an octad or 16-set has a centralizer of the form 21+8.O8+(2), a maximal subgroup.
|
|
The term octet is used to unambiguously specify a size of eight bits. It is used extensively in protocol definitions. Historically, the term octad or octade was used to denote eight bits as well at least in Western Europe; however, this usage is no longer common. The exact origin of the term is unclear, but it can be found in British, Dutch, and German sources of the 1960s and 1970s, and throughout the documentation of Philips mainframe computers.
|
|
A year later the American Flying Disc Open (AFDO) Rochester, New York, the Octad in New Brunswick, New Jersey and the 1975 World Frisbee Championships, held at the Rose Bowl in Pasadena, California, adopted Westerfield and Kenners freestyle competition format as one of their events. Today this same freestyle event is now accepted as one of the premier events in Flying disc tournaments worldwide. The Freestyle Players Association was formed to oversee the competitive aspects of freestyle frisbee, and to help new players learn how to freestyle.
|
|
In addition to the NS meets, OCTAD, a multi-event competition that started in New Jersey, came under the auspices of the PFC and was held at Sedgley for several years. The golf portion of these tournaments took place in Sedgley proper and the other events were held on the large ball-golf driving range next to the course and on the large field north of Reservoir Drive. These tournaments attracted the top players from across the country, over 300 at one event. Players' packages for the competitors included everything from custom printed discs and shirts to visors and hats.
|
|
Nonetheless, his forces are eventually defeated in Indocine and STRIKE conducts their operations in the South China Sea, where LeMonde is discovered dealing with Napoleon Hwong (Philip Tan), head of a fictional Triad-like criminal organization known as the Octad. The player recruits mercenary Harding Cash (Jamie Donovan) in battling the pirate warlord in an attempt to recover the missing nuclear weapon. After defeating Hwong's forces, the player and Harding manage to capture and interrogate Hwong for information concerning the whereabouts of the nuke long enough before Hwong commits suicide. The player eventually heads to Pyongyang, North Korea, where the stolen nuke is located.
|
|
A year later, the American Flying Disc Open (AFDO) in Rochester, New York, the Octad, in New Brunswick, New Jersey and the 1975 World Frisbee Championships, held at the Rose Bowl in Pasadena, California, adopted Westerfield and Kenner's freestyle competition format as one of their new events. Today that same freestyle event is one of the premier events in flying disc tournaments worldwide. Jim Kenner and Ken Westerfield were inducted into the Inaugural Pioneer Class of the FPA Freestyle Disc Hall of Fame: > Their play, innovation and influence began in the formative years prior to > competition, and was critical to the origin of the competitive sport of > Freestyle The first Frisbee ever designed with a disc sport tournament identification. The 1972 Canadian Open Frisbee Championships, Toronto. Canada.
|
|
He recruited members and formed the Florence Frisbee Team, the first players from the South to venture to such established tournaments as the National Frisbee Tournament in Michigan and the Octad at Rutgers in New Jersey. That year Rutgers produced a grad student player named Dan "Stork" Roddick, his nickname coming from his amazing abilities during ultimate and freestyle play and Dan was also the editor of Flying Disc News magazine that circulated along the East Coast. Wham-O recruited Dan to become the new director of the International Frisbee Association. His first order of business was to establish a network of reliable frisbee players around the country who could organize and run events by driving across America for recruits.
|
|
Westerfield helped to popularize Frisbee as an alternative disc sport in the 1960s and 70s. Delaveaga Park, Santa Cruz, CA. There were a few guts and distance competitions in the 1960s but disc sports really began in the early 1970s. The IFT guts Frisbee competitions in Northern Michigan, the Canadian Open Frisbee Championships, Toronto, ON (1972), the Vancouver Open Frisbee Championships, Vancouver, BC (1974), the Octad, New Brunswick, NJ (1974), the American Flying Disc Open (AFDO), Rochester, NY (1974) and the WFC, Rose Bowl, Pasadena, CA (1974), were the earliest Frisbee competitions to introduce the Frisbee as a new disc sport, up until these tournaments, the Frisbee was used as recreation and generally considered to be a toy. Westerfield and Kenner teamed up with Humber College professor Andrew Davidson, early Canadian disc sport promoter and Jeff Otis, event coordinator for the Canadian National Exhibition (CNE), to produce the Canadian Open Frisbee Championships (1972-1985).
|
|