Topic
Even code
About: Even code is a research topic. Over the lifetime, 33 publications have been published within this topic receiving 572 citations.
Papers
TL;DR: It is shown that the topology of the Adinkra is uniquely determined by a doubly even code, which results in an enumeration of these AdinkRA topologies up to N=28, and for minimal supermultiplets, up toN=32.
Abstract: Adinkras are diagrams that describe many useful supermultiplets in D = 1 dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N = 28, and for minimal supermultiplets, up to N = 32.
84 citations
TL;DR: In this paper, it was shown that the topology of an Adinkra is uniquely determined by a doubly even code and that every doubly-even code produces a possible topology.
Abstract: Adinkras are diagrams that describe many useful supermultiplets in D=1 dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N=28, and for minimal supermultiplets, up to N=32.
57 citations
TL;DR: The author introduces a special class of primitive BCH codes, the minimal BCH (MB) codes, and proves that an MB code has as minimum distance its designed distance and proposes a lower bound, sometimes tight, for the minimum distance of the dual.
Abstract: The author introduces a special class of primitive BCH codes, the minimal BCH (MB) codes. It is proved that an MB code has as minimum distance its designed distance. Using the Roos bound, the author proposes a lower bound, sometimes tight, for the minimum distance of the dual of an MB code. He describes the subclass of weakly self-dual extended MB codes and then characterizes some weakly self-dual extended BCH codes. Similarly, he proves that the nontrivial extended MB code over GF(4) is the smallest extended BCH code which is not an even code. He points out that extended MB codes are principal ideals of a modular algebra. >
56 citations
TL;DR: This work shows how two doubly even codes of lengths m1 and m2 can be combined to make a triply even code of length m1+m2, and proves that there are exactly ten maximal triplyEven codes of length 48 up to equivalence.
Abstract: A triply even code is a binary linear code in which the weight of every codeword is divisible by 8. We show how two doubly even codes of lengths m_1 and m_2 can be combined to make a triply even code of length m_1+m_2, and then prove that every maximal triply even code of length 48 can be obtained by combining two doubly even codes of length 24 in a certain way. Using this result, we show that there are exactly 10 maximal triply even codes of length 48 up to equivalence.
45 citations
TL;DR: It is shown that 17 is also not possible by reducing the problem to the consideration of 16 and finding a weight 12 vector, by computer, in each of these codes.
Abstract: It is an interesting open question whether an extremal (72, 36, 16) doubly even code C exists. In [3] the odd prime numbers which can divide the order of the group of C were determined. The largest of these, 23, was eliminated by finding weight 12 vectors in 384 codes [8]. The next largest prime remaining is 17. It is shown that 17 is also not possible by reducing the problem to the consideration of 16.17^{3} codes and then finding a weight 12 vector, by computer, in each of these codes.
30 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2017 | 1 |
| 2016 | 1 |
| 2012 | 4 |
| 2011 | 3 |
| 2010 | 1 |