Distance bounds for algebraic geometric codes

In this paper we consider the Suzuki curve y q + y = x q 0 (x q + x) over the field with q = 2 2m+1 elements. The automorphism group of this curve is known to be the Suzuki group Sz(q) with q 2 (q − 1)(q 2 + 1) elements. We construct AG codes over F q 4 from an Sz(q)-invariant divisor D, giving an explicit basis for the Riemann-Roch space L( D) for 0 < ≤ q 2 − 1. The full Suzuki group Sz(q) acts faithfully on each code. These families of codes have very good parameters and information rate close to 1. In addition, they are explicitly constructed. The dual codes of these families are of the same kind if 2g − 1 ≤ ≤ q 2 − 1.

Section: Theorem 4 the Minimum Distance D Of The Code C M = C L (E supporting

confidence: 63%

“…(15). Therefore, there will be no improvement using Theorem 6.1 and thus we get no improvement with all order-bounds in [7] and [2].…”

Section: Examplementioning

confidence: 95%

Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Matrix theory for minimal trellises

Duursma

2019

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