A Construction of New MDS Symbol-Pair Codes

Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes

“…First, we consider the construction of MDS symbol-pair codes with d p = 5, which extends the results of [7,Theorem 16] and [7,Theorem 19].…”

“…This proposition is an essential ingredient for the constructions in [7] (see [7,Lemma 5]). In the following, we will employ cyclic and constacyclic codes to generate MDS symbol-pair codes.…”

“…In particular, we focus on the construction of (n, d p ) q MDS symbol-pair code whose minimum pair-distance d p is small. The known parameters of (n, d p ) q MDS symbol-pair codes with small d p are the following ones: a) q ≥ 2, n ≥ 2, d p ∈ {2, 3} [4], b) q ≥ 2, n ≥ 4, d p = 4 [4], c1) q is an even prime power, n ≤ q + 2, d p = 5 [4], c2) q is an odd prime, 5 ≤ n ≤ 2q + 3, d p = 5 [4], c3) q is a prime power, n | q 2 − 1, n > q + 1, d p = 5 [7], c4) q is a prime power, n = q 2 + q + 1, d p = 5 [7], c5) q ≡ 1 (mod 3) is a prime power, n = q 2 +q+1 3 , d p = 5 [7], d1) q is a prime power, n = q 2 + 1, d p = 6 [7], d2) q is an odd prime power, n = q 2 +1 2 , d p = 6 [7], e) q is an odd prime, n = 8, d p = 7 [4].…”

List Decodability of Symbol-Pair Codes

“…Chee et al [4] established a Singleton-type bound and showed the existence of symbol-pair codes meeting this bound. Following this direction, several works contributed to the constructions of symbol-pair codes meeting this bound [5] and [13].…”

Maximum distance separable codes for b-symbol read channels

“…Cassuto and Blaum [1] first proposed a new coding framework for symbol-pair read channels. For a complete comprehension of the fruitful results on this topic, please refer to [1,2,3,4,5,6,7,9] and the references therein. Recently, Yaakobi et al [10] generalized the coding framework for symbol-pair read channels to that for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols.…”